Add 1⁄4 cup of the olive oil, the olives, capers, tomatoes, and thyme into the pan.

Cook, stirring occasionally, until a thickish sauce is formed but the tomatoes still retain their shape, about 5 minutes. Transfer the sauce to the edges of your serving platter, and wipe the pan clean with a paper towel.

Place the pan back over high heat. While it’s heating, rub the tuna steaks with the remaining olive oil and the pepper.

When the pan is smoking hot, place the tuna steaks in it in a single layer (if necessary, do it in two batches).

Cook the tuna for about 3 minutes, until it turns white halfway up the sides.

Flip and cook until just a tiny bit of pink remains on all sides, another 2 minutes or so (for medium rare).

Slice the tuna on a cutting board into 1⁄4" slices. Arrange in the center of the serving platter.